C. S. Helvig, Gabriel Robins, and Alexander Zelikovsky. Improved approximation bounds for the group Steiner problem. In Proc. Conference on Design Automation and Test in Europe, pages 406--413, Paris, France, February 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for the rectilinear problem, as well as for other geometric versions. The group Steiner tree problem in graphs cannot be approximated better than a factor ln k in polynomial time, assuming P 6= NP [4, 15] Several (polynomial time) approximation algorithms have been proposed for the problem [3, 7, 11, 15, 17, 23]. The best guarantee found which is independent of n is O(k ffl ) for any fixed ffl 0 [11] A poly logarithmic bound of O(log 2 n log k log log n) was recently given by Charikar et al. 3] This sophisticated algorithm uses a linear programming relaxation of the problem which is mapped into ....

.... cannot be approximated better than a factor ln k in polynomial time, assuming P 6= NP [4, 15] Several (polynomial time) approximation algorithms have been proposed for the problem [3, 7, 11, 15, 17, 23] The best guarantee found which is independent of n is O(k ffl ) for any fixed ffl 0 [11]. A poly logarithmic bound of O(log 2 n log k log log n) was recently given by Charikar et al. 3] This sophisticated algorithm uses a linear programming relaxation of the problem which is mapped into an integer solution by deterministic rounding techniques. If the number of vertices in each ....

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C. S. Helvig, G. Robins, and A. Zelikovsky. Improved Approximation Bounds for the Group Steiner Problem. In Proc. Conference on Design Automation and Test in Europe, pages 406--413, 1998.

....robins cs.virginia.edu, 804) 982 2207, http: www.cs. virginia.edu robins 1 Optional Steiner nodes may be included in order to reduce the cost of the spanning tree interconnecting the groups of N (see Figure 1) The Group Steiner Problem captures practical scenarios in VLSI circuit design [4, 9, 19], where circuit modules may be rotated and flipped when positioned on a VLSI chip. This induces multiple potential connection points for a given circuit module, namely, one for each of the eight possible orientations [4, 19] see Figure 1(b) These locations correspond to a group of up to eight ....

....performance ratio 1 of O(k ffl ) for any fixed ffl 0, where k is the number of groups. On the negative side, it is known that this problem cannot be efficiently approximated with a performance ratio of less than ln k times the optimal [7, 12] Our work has appeared in preliminary form in [4, 9]. The organization of the remainder of this paper is as follows. Section 2 introduces depth d bounded Steiner trees and proves that they approximate the optimal group Steiner tree to within a factor of 2d Delta d p k. Section 3 presents our main heuristic for approximating optimal depth d ....

C. S. Helvig, Gabriel Robins, and Alexander Zelikovsky. Improved approximation bounds for the group Steiner problem. In Proc. Conference on Design Automation and Test in Europe, pages 406--413, Paris, France, February 1998.

....given an undirected weighted graph G = V; E) and M V , find a minimum cost tree which spans all of M . This work was supported by a Packard Foundation Fellowship and by National Science Foundation Young Investigator Award MIP 9457412. A preliminary version of this work has appeared in [3] [8]. The corresponding author is Professor Gabriel Robins, Department of Computer Science, University of Virginia, Charlottesville, VA 22903 2442, robins cs.virginia.edu, 804) 982 2207, http: www.cs.virginia.edu robins 1 Nodes in V Gamma M (referred to as Steiner nodes) may be optionally ....

....6 extends our basic group Steiner approach into a bounded radius formulation that minimizes tree cost as well as source to sink pathlengths in a provably good manner. Finally, we discuss our implementation and experimental results in Section 7. A preliminary version of this work appeared in [3] [8]. 2 Depth Bounded Steiner Trees In this section, we introduce the concept of Steiner depth bounded 5 trees. Our motivation for using depth bounded trees is two fold: 1) optimal depth 2 bounded trees can be used to approximate optimal group Steiner trees to within a factor of 2 Delta p k, and ....

C. S. Helvig, Gabriel Robins, and Alexander Zelikovsky. Improved approximation bounds for the group Steiner problem. In Proc. Conference on Design Automation and Test in Europe, pages 406--413, Paris, France, February 1998.

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